I am currently in the Military stationed in OH but my home of record and where I file state tax returns is CA. On the W2, Item 17, Sate Income tax it shows no amount but on my LES (monthly income statement) it clearly shows me paying taxes to California. I am married and filing jointly but my wife works in Ohio but is also resident of California. (We submit an IT10 showing we pay taxes in CA). So if I am paying taxes to California every month which shows on my LES but it doesn't show up on line 17 of the W2 why would I owe the state of CA 380.00? (My state wages in line 16 are there and correct).
If you are stationed in OH on PCS orders then both of you are, for Calif tax purposes, nonresidents of Calif. So, Calif can only tax Calif-source income such as from a rental property there. If you have no Calif-source income then you don't need to file a Calif return at all unless you have paid in some 2016 Calif taxes via withholding or whatever. In that case you would file nonresident Calif Form 540NR, declaring 0 Calif-source income (in Nonresident Adjustments) to get a full refund.
See California's publication 1032, Tax Information for Military Personnel, here
You can find your scenario in Example 6 on page 8. Instruction D has good info as well.